Liquidity Risk under the EMIR
Regulation
Master Thesis
Author: David Kühnl Supervisor: Esther Eiling Month and Year: July 2016
This document is written by Student David Kühnl who declares to take full re-sponsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Amsterdam, July 7, 2016
I am grateful especially to my supervisor Esther Eiling for her kind guidance and helpful advice.
This thesis was written within a thesis internship at Ortec Finance. I would hereby like to thank all my former colleagues for providing me with valuable experience and especially Patrick Tuijp for his insight, interesting comments, and overall sup-port.
This thesis investigates the potential liquidity risks pension funds may face once they adapt to the EMIR regulation in 2017. The regulation imposes rules on cen-tral clearing and collateralization of the interest rate derivatives which the pen-sion funds use to hedge against interest rate risk. One particular rule is that the margin calls on these derivatives should be filled in cash only. I therefore focus on possible strategies how to approach the cash-only rule. Namely, I investigate liquidity properties of the assets that could be used to obtain cash for the margin calls. First, I find a moderate negative correlation between liquidity and margin calls. Later, employing a probit model and a VAR model, I find interest rates to be the link between margin calls and liquidity. Finally, I show that a shock to the interest rate big enough to cause a margin call indeed has a significant negative impact on the liquidity. However, I find that the magnitude of the change in the liquidity is rather small. I therefore conclude that pension funds do not face any significant liquidity risks while selling their assets to fill a margin call.
JEL Classification G11, G12, G18, G23
Keywords EMIR, Liquidity, Pension Funds, VAR
List of Tables vii
List of Figures viii
1 Introduction 1
2 Literature Review 4
2.1 European Market Infrastructure Regulation . . . 4
2.2 Approaches to Liquidity Risk . . . 4
2.3 Pension Funds and EMIR . . . 5
2.4 Liquidity-Return Trade-off . . . 5
2.5 Current Issue . . . 7
2.6 Liquidity Drivers . . . 7
2.7 Link to Margin Calls . . . 9
3 Data 10 3.1 Pension Funds . . . 10
3.2 Margin Calls . . . 11
3.3 Liquidity . . . 14
3.3.1 Initial Universe of Assets . . . 14
3.3.2 Liquidity Measures . . . 15
3.3.3 Sample Construction . . . 16
3.4 Liquidity Drivers . . . 18
3.4.1 Interest Rate Based Variables . . . 20
3.4.2 Equity Based variables . . . 20
3.4.3 Macroeconomic Indicators . . . 20
3.4.4 Seasonality Variables . . . 21
4 Methodology 25 4.1 Correlation . . . 25
4.2 Probit Model . . . 26
4.3 VAR Model . . . 28
5 Results 31 5.1 Correlation of Margin Calls and Liquidity . . . 31
5.2 Margin Calls and Liquidity Drivers . . . 35
5.3 Liquidity – VAR Model . . . 38
5.3.1 Liquidity Drivers – Static . . . 38
5.3.2 Commonality and Spillovers – Dynamic . . . 41
5.3.3 The Big Picture . . . 41
6 Robustness 47 6.1 Margin Account Specification . . . 47
6.2 Scale Independence of Correlation . . . 50
6.3 Stationarity . . . 51
7 Conclusion 54
Bibliography 57
A Data I
A.1 Margin Calls Variable . . . I A.2 Liquidity . . . V A.3 Miscellaneous Tables . . . XI
3.1 Margin Calls Descriptive Statistics . . . 14
3.2 Descriptive Statistics of Liquidity Data . . . 19
3.3 Overview of Liquidity Drivers . . . 21
3.4 Descriptive Statistics of Selected Liquidity Drivers . . . 23
5.1 Detailed Overview of Correlations . . . 34
5.2 Margin Calls and Liquidity Drivers – Probit Results . . . 36
5.3 Liquidity Drivers – VAR Exogenous Part . . . 39
5.4 Commonality and Spillovers – VAR Endogenous Part . . . 42
6.1 Robustness of Probit Results . . . 48
6.2 Results of Augmented Dickey-Fuller Test . . . 53
A.1 Available YC maturities . . . II A.2 Overview of Data Processing . . . XI A.3 Inter-group Correlations . . . XII A.4 Data Sources - Overnight Rate . . . XIII A.5 Data Sources - Bonds and Equities . . . XIV A.6 Additional Results of the Augmented Dickey-Fuller Test . . . XV
3.1 Margin Calls Dummy Construction . . . 13
3.2 Geographic Distribution of Assets . . . 15
3.3 Liquidity Depending on Price and Volatility . . . 17
5.1 Correlation of Margin Calls and Liquidity . . . 32
5.2 Effects of Shock to European Liquidity . . . 43
5.3 Effects of Shock to European Overnight Rate . . . 44
5.4 Effects of Shock to European Term Spread . . . 45
A.1 Semi-annually Interpolated Yield Curve . . . III A.2 Historical Swap DV01 . . . IV A.3 Margin Account Sensitivity . . . VI A.4 Corwin Spread Estimation . . . VII A.5 Data Downloading Algorithm . . . IX A.6 Data Processing Algorithm . . . X
Introduction
Due to their capability of leverage and ability to flexibly transform payoff and risk of the underlying security, derivatives are broadly used for hedging purposes. Some of them, especially those with complex and opaque structures or those allowing extensive use of leverage, can potentially introduce a significant coun-terparty risk (Luettringhaus, 2012). While the standardized, on-exchange-traded derivatives are subject to regulation, the over-the-counter (OTC) market is rather non-standardized and decentralized in the sense that the deals result solely from the bilateral negotiations between the involved parties.
Introduced by the Council of European Union (2014), the European Market Infrastructure Regulation (EMIR) has an ambition to mitigate the risk arising from the OTC market by imposing rules on clearing and collateralization. Most of the deals should be cleared through central clearing counterparties and the rest should be at least subject to standardized margin requirements. One of the key aspects of EMIR is that the posted collateral should be sufficiently liquid. In case of the cen-tral clearing, not even securities like high-rated bonds should be used any more. The only eligible instrument for the variation margin is now cash.
The cash-only-collateral rule might be crucial especially for institutions, e.g. pension funds, that tend to limit the amount of cash they hold as it bears no in-terest. At the same time, pension funds usually have long-term liabilities, value of which is sensitive to changes in the long-term interest rate. More precisely, when the interest rate decreases, the present value of these liabilities increases due to a lower discounting factor. Pension funds therefore usually hedge their liabilities against the decrease in the long-term interest rates using interest rate derivatives such as interest rate swaps. Consequently the pension funds might be subject to a margin call on the position in the derivatives when the interest rate increases. So
far, the pension funds were allowed to take the assets they hold and post them as a collateral incurring no additional costs. However, once the exemption for pen-sion funds is lifted (supposedly in 2017), they will be obliged to actually sell part of the assets and post the cash proceeds as the collateral instead.
Meanwhile, the interest rate is also known to drive liquidity in equity and bond markets. In particular, Chordia et al. (2001) show that an increase in interest rate has a negative impact on liquidity and trading activity. The liquidity may there-fore dry up exactly when the pension funds receive a margin call. Under such a scenario, the pension funds may face a significant liquidity risk and incur consid-erable costs while selling off their assets in order to obtain cash to fill the margin call. Alternatively, they may incur the opportunity cost of holding more cash in the first place.
The goal of this thesis is to analyse the potential liquidity risk the pension funds might face in case a margin call on their position in derivatives occurs. The topic may also reveal certain important policy implications of the EMIR regula-tion. For instance, the pension funds might be forced to significantly alter their portfolio allocation which may actually harm their funding ratios. The main re-search question of this thesis is therefore the following:
Do pension funds face a significant liquidity risk under the EMIR regulation posed by the Council of European Union?
There is an extensive body of literature on the topic of liquidity. However, since EMIR is a current issue and the pension funds are still exempted, studies of its possible implications are scarce. My ambition is to build on the existing research about liquidity and link it to the topic of interest rate hedging and margin calls in the context of pension funds’ asset-liability management.
One of the challenges of this thesis is that pension funds currently have an exemption from EMIR which is supposed to be lifted no sooner than in 2017. I therefore conduct an ex-ante research. I apply the rules imposed by EMIR on the past data and I investigate what would happen if EMIR was already effective for the pension funds. First, a variable describing when the margin calls would have likely happened is constructed based on the historical interest rates. Then, I in-spect the correlation of this variable with the liquidity of equities divided into ge-ographic categories identified based on the balance sheets of the pension funds. Further, I use a probit model to identify the variables that drive the margin calls. Finally, I use a VAR model to jointly analyze liquidity of the different assets the
pension funds hold and to find whether the variables behind margin calls also af-fect liquidity. The results are then used to analyze the liquidity impact of a shock to one of the drivers. Based on the response of the liquidity to such a shock, one can draw conclusions whether the pension funds face a serious liquidity risk and whether they should be maintaining a cash buffer to cover the potential margin calls.
In the end, I find that there is a significant relationship between liquidity and margin calls driven by the interest rates. The magnitude of this relationship how-ever seems to be rather small. More precisely, the response to an interest rate shock related to a margin call does not exceed the daily standard deviation of the liquidity. I therefore cannot conclude that the pension funds face a significant liquidity risk under the EMIR regulation. One possible reason might be that un-der EMIR, the margin accounts are rather sensitive. Consequently, the implied change in interest rate leading to a margin call is small and so is the liquidity re-sponse. Such a design could then secure low counterparty risk by frequent ex-change of margin while not introducing any liquidity risk which is, in essence, the main goal of the EMIR regulation.
The rest of the thesis is structured as follows. Chapter 2 provides an overview of the current research relevant to the topic and describes the position of this thesis in the existing literature. Chapter 3 summarizes the variables used in the analysis and describes the way they are constructed from the underlying data. In Chapter 4, I explain the methods and models used for the empirical analysis. Chapter 5 then summarizes the results of the empirical analysis. The robustness of the results is discussed in Chapter 6. Finally, Chapter 7 contains the conclud-ing remarks. I provide an overview of the main results and their implications. I also discuss the limitations of the thesis and I provide suggestions for further re-search.
Literature Review
2.1 European Market Infrastructure Regulation
The motivation behind this thesis is the European Market Infrastructure Regula-tion (EMIR) imposed by the Council of European Union (2014). It came into force on August 16, 2012. However, it contains an exemption for pension funds which is supposed to be lifted no sooner than in 2017. The ambition of the regulation is to establish a framework, based on central clearing and collateral requirements, in order to mitigate risk arising from the decentralized bilateral deals in the OTC derivatives market. In particular, EMIR imposes a set of strict rules on the mar-gin accounts that should be maintained along with the positions in derivatives. First, it specifies how to compute the size of the initial margin when the position is opened. Second, it specifies the threshold and the form of the variation margin which should be transferred between the counterparties as the value of the posi-tion changes. The threshold, above which the margin transfer is mandatory, is set to 500,000 Euro and what is more important, the eligible form of such a margin is agreed to be cash only.
2.2 Approaches to Liquidity Risk
Implementation of the EMIR regulation could indeed improve stability of the OTC market by bringing more transparency which is otherwise lacking due to the pri-vate nature of the usual bilateral agreements (Luettringhaus, 2012). Furthermore, Johannes and Sundaresan (2007) and Tuckman and Serrat (2011) argue that credit enhancements and mark-to-market margin mitigate the counterparty default risk and ISDA (1999) reports cash to be the most widely accepted form of collateral
anyway. In the same paper however, Johannes and Sundaresan (2007) emphasize that the cash buffer could be otherwise invested in the money market and earn at least the short-term risk free interest rate. That suggests a trade-off between holding cash reserves and earning positive return. Such a trade-off might be cru-cial especru-cially for pension funds whose task to maintain a decent funding ratios can be particularly difficult in the current low-yield environment (Antolin et al., 2011). On the other hand, with the short-term interest rates recently becoming negative, the opportunity cost of holding a cash buffer rather than investing in the money market diminished as well.
2.3 Pension Funds and EMIR
The link between pension funds and the EMIR regulation is through the asset-liability management they employ. As was mentioned in Chapter 1, pension funds have long term liabilities which leave them exposed to an interest rate risk. Ve-ronesi (2010) shows, that it is possible to hedge against the interest rate risk by cash-flow matching or by duration hedging. Bikker et al. (2012) report that the pension funds typically have a liabilities with duration between 15 and 20 years. The lower durations are usually hedged by constructing a fixed income portfolio of bonds. Such a portfolio then generates sufficient cash flows exactly at the times of maturity of the liabilities. The rest of the risk can be hedged using a position in interest rate derivatives such as swaps (Chernenko and Faulkender, 2012), which are OTC traded instruments falling under the EMIR regulation.
2.4 Liquidity-Return Trade-off
The liquidity-return trade-off has been studied from many angles in the recent past. For instance Duffie and Ziegler (2003) investigate several different strategies how to approach liquidity risk. In particular, they use a model with three types of assets (illiquid, liquid and cash) and they compare outcomes of different strate-gies depending on the pecking order of the assets in case of liquidation. They show that holding a last resort buffer of cash and liquid assets is relatively more costly but it significantly decreases the insolvency risk, while holding the illiquid asset is less costly but it can result in high tail losses or even insolvency in the case of extremely high volatility. In the light of their results, reallocating part of the portfolio into a relatively liquid asset might seem as a reasonable compromise.
Amihud and Mendelson (1986) came up with an asset pricing model related to the liquidity of the assets and show that expected returns are increasing and concave function of the bid-ask spreads. That is, investing into liquid assets leads to lower returns. Sadka (2010) and Aragon (2007) then show that funds investing into illiquid assets indeed generate on average 4% to 6% higher annual return than those investing into more liquid assets.
Furthermore Amihud (2002) shows, using a time series analysis, that the gen-eral level of liquidity predicts the excess returns of equities. In particular, he shows that increased illiquidity implies increased return. That suggests that the liquidity-risk premium might be one of the components of the overall risk pre-mium commanded by equities. Acharya and Pedersen (2005) then use a liquidity-adjusted CAPM and show that the expected return of a security depends on the liquidity of the given security and also on the covariance of the liquidity and re-turn of such a security with the general market rere-turn and liquidity.
Holmstrom and Tirole (2001) introduce a liquidity-based asset pricing model and show that in times of general illiquidity, the liquid assets command a liquidity premium. More precisely, they compare the liquidity premium to a put option on the liquidity itself. The pay-off of a put option then implies that the lower the liquidity is, the higher is the liquidity premium. Suppose that margin calls occur in times when liquidity is low in general, but there are some sufficiently liquid assets. Then, holding the liquid assets instead of cash might be favourable as they can be sold at premium exactly when needed.
One of the potential downsides of a strategy relying on selling off assets to fill the margin call is described in paper by Chordia et al. (2008). They argue that in an illiquid market, market efficiency could decrease rapidly and therefore a sig-nificant mispricing may arise. The argument is based on their previous research showing a positive correlation between liquidity and trading activity. Low trading activity limits the ability of arbitrageurs to exploit a potential mispricing. That implies slower discovery of the true price and consequently, apart from incurring high transaction costs, the pension funds might be forced to sell their assets far from the fair value. Such a failure of market efficiency would then mean addi-tional costs when filling the margin call.
The overview above suggests that the pension funds have several different op-tions how to approach the problem they face. Generally, the approaches differ in the degree of liquidity of the last-resort cushion set aside to fill the potential margin calls. The two extreme cases are either to set up a cash reserve or to not
alter the portfolio allocation at all. The former would probably lead to lower re-turns, the latter, on the other hand, could result in a significant liquidity risk when the margin call occurs. Clearly, the outcomes of the different approaches differ and more importantly, they depend on the liquidity conditions of the given situ-ation. While there are a lot of studies about liquidity in general, it has not been intensively studied in the context of margin calls yet. This thesis therefore builds on the existing literature and aims to link the liquidity to the margin calls what would help to evaluate the viability of the distinct strategies the pension funds may employ.
2.5 Current Issue
The topic recently gained importance also in the Netherlands in particular. De Nederlandsche Bank states in its Supervision Outlook (2016) that the adaptation to the EMIR regulation is one of their top priorities for the following few years. Furthermore, as mentioned in Bikker et al. (2012), the Dutch pension funds cover almost the entire labour force which accounts for about 46%1of the total popu-lation of the country. I will therefore base my research on information taken from the actual balance sheets of three large Dutch pension funds.
2.6 Liquidity Drivers
There is an extensive body of literature related to the topic of liquidity which can be used to uncover the potential links between liquidity and margin calls.
For instance, Glosten and Milgrom (1985) model explains the adverse selec-tion problem faced by the dealers providing liquidity to the financial markets. They show that the dealers compensate for trading with informed traders by quot-ing wider spreads resultquot-ing in higher transaction costs. Chordia et al. (2001) point out the difficulty of employing such a framework on the level of individual as-sets. However, they expect an increased level of informed trading surrounding announcements of various macroeconomic indicators and suggest using dummy variables denoting these announcements while modelling liquidity. Expanding their suggestion, I also incorporate the difference between the announced value and the prior expectation to account for the magnitude of the superior informa-tion the informed traders poses.
According to Stoll (1978), dealers also face an inventory risk in the sense that they need to hold a sufficient amount of assets to be able to flexibly provide liq-uidity to the market. However, the future value of the inventory is uncertain and depends on market volatility. The dealers demand compensation for the inven-tory risk by quoting wider spreads which again increases the transaction costs. Later, Ho and Stoll (1981) expand the inventory risk model and show that also the short-term interest rate drives the inventory risk as it represents the cost of financing the inventories and also the cost of trading on margin.
The long-term interest rate matters for the liquidity as well. For instance, Ehrmann et al. (2011) show that an increase in the long-term interest rate leads to a spillover towards the bond market as the investors reallocate their portfolios to capture the relatively high yields. Such a transmission could result in lower trading activity in the equity market which is, as shown in Chordia et al. (2001), correlated with lower liquidity. Furthermore, Hameed et al. (2010) link the mar-ket liquidity to funding liquidity and show a liquidity deterioration in declining markets. They argue that poor market-wide performance increases the inventory risk as when the asset prices are on decline, it becomes more and more costly to unwind positions if necessary and the dealers therefore demand additional com-pensation for holding inventory.
Authors like DellaVigna and Pollet (2009) link market activity with the be-havioural motives and investors’ mood fluctuation. They, for instance, show a decreased market activity on Fridays which could, assuming negative correla-tion between liquidity and trading activity (Chordia et al., 2001), also imply a de-creased liquidity on Fridays.
Finally, Chordia et al. (2001) build on the theoretical models for liquidity and, using an extensive sample of US equities, they identify a number of variables driv-ing liquidity and traddriv-ing activity. They empirically show a significant negative im-pact of changes in the short-term and the long-term interest rate on the liquidity and trading activity. They also document the liquidity deterioration in declining markets and they reveal certain seasonality patterns in the trading activity. Fur-ther, Chordia et al. (2005) study the time-series properties of liquidity of US stocks and bonds using a VAR model. They find a significant commonality in the liq-uidity of stocks and bonds. More precisely, they document a correlation of 31%. Additionally they find the liquidity to be negatively correlated with the returns on the assets.
2.7 Link to Margin Calls
This thesis aims to combine and expand the methods employed in Chordia et al. (2001) and Chordia et al. (2005). In particular, I build a VAR model with exogenous variables which allows to model the liquidity of the individual groups of assets and then allow the groups to affect each other. The goal is then to analyze liquidity of the individual groups and link it to margin calls on the derivatives the pension funds hold.
One way how to link the liquidity to the margin calls is to look for their com-mon drivers. The liquidity drivers can be identified based on the existing research summarized above. To identify the drivers of the margin calls, one can rely on the research related to the field of fixed income securities.
Veronesi (2010) or Tuckman and Serrat (2011) provide a sufficient description of interest rate swap contracts. They show decomposition of a swap contract into a portfolio of fixed-rate bond and floating-rate bond. Further, they show how to approximate the changes in the value of such bonds using the concept of dura-tion. Consequently, one is able to approximate the change in the value of the whole swap contract as well. Putting it together with the rules imposed by the Council of European Union (2014) in EMIR, we can investigate the dynamics of the margin account depending on the swap rates.
∗ ∗ ∗
There are multiple theoretical frameworks for modelling liquidity based on the behavior of the market dealers and investors. Theoretical approaches to liq-uidity risk are also well-documented and many asset pricing models take liqliq-uidity component into account as well. There are also many empirical studies analyz-ing liquidity of various assets both in cross-section and time-series. The topic of liquidity is covered in literature extensively. So are the OTC markets and the inter-est rate derivatives. There is an existing discussion about the possible advantages and disadvantages of a central clearing and collateralization. The mechanics of the interest rate swaps and their valuation is described in detail as well.
However, research which would explicitly link market liquidity and margin calls on interest rate derivatives is rather scarce. Since the EMIR regulation in-creases the importance of liquidity in the context of the margin calls by imposing the cash-only collateral rule, extending the research in this field seems to be ap-propriate.
Data
In this section, I describe the data I use in the analysis. First, Section 3.1 describes data on the balance sheets of the pension funds. Section 3.2 describes construc-tion of the proxy variable for the margin calls. Then, Secconstruc-tion 3.3 shows how I estimate the bid-ask spreads which reflect the liquidity of the pension funds held assets. Finally, Section 3.4 contains description of the variables that were shown to drive the liquidity in general and that could possibly drive the margin calls as well.
3.1 Pension Funds
My dataset is constructed based on the information extracted from balance sheets of three large Dutch pension funds. In particular, for each of the pension funds, I have the actual relative asset allocation by the end of 2015. The assets are divided into a Matching portfolio and into a Return portfolio.
The matching portfolio consists of government bonds and investment-grade corporate bonds. However as explained later, the matching portfolio not only generates returns but also figures as hedge against interest rate risk via the cash-flow matching (Veronesi, 2010). I therefore focus primarily on the return portfolio. The return portfolio consist mostly of stocks and it is further divided into cat-egories determined by geographic location of the stocks. The data on the return portfolio also contain information about the relative asset allocation between those geographic categories. However, since the information I have is only a snap-shot at the end of 2015 and since the period I focus on covers about 10 years, I cannot assume a constant asset allocation over the period. Moreover, the asset allocation also varies depending on the given pension fund. To make the research
more general and robust, I therefore do not use the actual allocation and I only focus on the geographic groups.
3.2 Margin Calls
Since I aim to analyze the liquidity risk the pension funds may face when they receive a margin call on their position in interest rate swaps, a crucial step of this thesis is to identify when the margin calls are likely to happen given the rules established in EMIR.
First, when a swap position is opened, an initial margin is transferred to the counterparty to cover the initial risk exposure of such a position. The size and computation of the initial margin is specified by Basel Committee on Banking Supervision (BCBS, 2015).
Once the position is set and the initial margin is transferred, the value of the position is marked-to-market on a daily basis. As the value of the position chan-ges, if necessary, a variation margin is exchanged between the parties to contin-uously offset the changing risk exposure (Council of European Union, 2014). To approximate the change in the value of an interest rate derivative, one can use the dollar duration of the derivative which says how much the value changes when the interest rate curve shifts by 1 percentage point (p.p.).
The question is, when exactly is the variation margin exchanged. There are two possible approaches. First, EMIR specifies a maximum threshold of 500,000 Euro which, when exceeded, triggers a mandatory transfer of the variation mar-gin. One can therefore assume that once the value of the position decreases by more than 500,000 Euro, a margin call occurs. Under such an assumption, we can compute the sensitivity of the margin account to the interest rate changes as
Sensitivity = 500000
D$· #Swaps . (3.1)
A potential drawback of this method is that one need an information about the properties of the actual swap contract that is being used in the given case.
Second, a more robust approach is based on a relative margin threshold. A common practice when trading on a margin account is, that margin call occurs once the margin account decreases under certain threshold, for instance 90%. Putting this assumption together with the specification of the initial margin, one
can approximate the sensitivity of the margin account to the interest rate change as follows
Sensitivity =DurBracket · (0.4 + 0.6 · NGR)(1 − Threshold)
D$· SwapFace−1 , (3.2)
where NGR reflects the degree of counterparty risk and DurBracket reflects the risk of the given derivative. The parameters are defined in BCBS (2015). One of the advantages of this approach is that, as explained in Section A.1, it does not require any information about the actual position in the swap contracts because it cancels out when we compute the initial margin. The only thing one needs to do is to assume a generic swap contract and compute the respective dollar duration as described below.
In the both cases, the sensitivity says how much the interest rate can increase before the margin call is initiated. I then use it together with the time series of the interest rates to identify when the margin calls are likely to happen.
A key element of the margin account sensitivity is the dollar duration of the swap contract. Since the dollar duration depends on the current yield curve and since my sample covers more than 10 years, I cannot assume a constant dollar duration. I therefore use the historical yield curve to approximate the dollar du-ration on a monthly basis. Using the dynamic dollar dudu-ration then implies that the sensitivity of the margin account will be dynamic as well.
Finally, I obtain the sensitivity by plugging the dollar duration either into (3.1) or into (3.2). I then use the obtained sensitivity to construct the margin calls dummy variable. The process is as follows. At a given time, the margin account is fixed at certain level of the interest rate. Then, as the interest rate changes and consequently the value of the swap contract change, two scenarios may arise. First, the interest rate decreases and the contract gains value. In this case, the margin account is fixed at the new level of the interest rate and the process is repeated from the beginning. Second, if the interest rate increases, the position loses value and the initial margin is being depleted. Once the interest rate change exceeds the threshold given by the sensitivity of the margin account, a margin call occurs. After the margin call is filled, the margin account is again fixed at the new interest rate level and the process is repeated from the beginning.
This way, I obtain the time series of dummy variable reflecting the margin call occurrences. Furthermore, I also obtain another variable, which reflects how the margin account is being depleted while the interest rate increases. Such a variable
could prove useful when analyzing the dynamics of the margin account, not only the margin calls themselves.
The whole procedure is illustrated by Figure 3.1 which depicts the construc-tion of the variable on a selected sub-sample.
Figure 3.1: Margin Calls Dummy Construction
Note: This figure depicts construction of the proxy variable for the margin calls. The solid green line represents the swap rate. The solid red line represents the margin level depending on the swap rate. The blue shaded area is the increase in the swap rate since the current margin level was last set. When the increase in the swap rate exceeds the sensitivity threshold (blue line), a margin call occurs (vertical dotted line) and the margin level is fixed at the new level. When the swap rate is decreasing, the margin level is decreasing as well as the excess funds are withdrawn from the margin account to be invested.
The descriptive statistics of the obtained variables are depicted in Table 3.1. Besides the variable constructed based on a 10% threshold which is used as the main independent variable, I also report the variables constructed based on 20% and 30% thresholds and also based on the absolute threshold of 500,000 Euro specified in EMIR. The alternative specifications are later used to check the ro-bustness of the results.
Table 3.1: Margin Calls Descriptive Statistics
variable mean median sd p25 p75 min max N
MC 10% 0.273 0 0.446 0 1 0 1 2876
MC 20% 0.157 0 0.364 0 0 0 1 2876
MC 30% 0.102 0 0.303 0 0 0 1 2876
MC TH 0.097 0 0.296 0 0 0 1 2876
D Spread 2.435 1.6 2.876 0 3.700 0 17.800 2869
Note: This table contains descriptive statistics of the main dependent variable and its alternative specifications. The main variable based on a 10% margin threshold is in the first row. The alternatives are based on 20% and 30% thresholds and on an absolute threshold of 500,000 Eur. According to the mean values, as we increase the margin threshold and thus decrease the sensitivity of the margin account, the average unconditional probability of margin call decreases from 27.3% to 9.7%. The last row describes the absolute value of the variable DSpread which is the daily first difference in the depletion of the margin account. It reflects the changes of the shaded area in Figure 3.1. Its mean value 2.435 suggests that on average, there is a daily change in the margin induced by a change of the interest rate by 2.435 basis points.
As visible in Table 3.1, the means and the standard deviations decrease with the increasing margin threshold. The relationship follows an intuition that as we allow more fluctuation in the margin account, the margin calls will occur less of-ten. More specifically, with the 10% threshold, a margin call will occur 27 times out of 100. As we increase the threshold to 30%, the number of the margin calls decreases to 10 out of 100. Further, the variable DSpread is the absolute value of the first difference in the depletion of the margin account denoted in basis points of the interest rate. Its mean value 2.435 suggests that on average there is a daily change in the margin depletion induced by an change of the interest rate by 2.435 basis points.
A more detailed description of the construction of the proxy variable for the margin calls is provided in Section A.1.
3.3 Liquidity
3.3.1 Initial Universe of Assets
I start by looking at the asset side of balance sheets of three Dutch pension funds to inspect the universe of assets they invest in. Generally, the assets suitable for liquidation are either stocks or bonds. As was mentioned in Chapter 2, bonds, as
a part of the fixed income matching portfolio, are partially hedging the interest rate risk along with the interest rate derivatives. I therefore assume that the pen-sion funds would start by selling the stocks first so they do not alter the hedging position if not necessary.
I identify 24 groups of stocks based on the location they reside in. I then use Bloomberg stock screening to identify the individual stocks from these ographic groups. The initial universe counts 49,198 individual stocks and the ge-ographic area they cover is depicted in Figure 3.2.
Figure 3.2: Geographic Distribution of Assets
Note: This figure shows the geographic distribution of the initial universe of assets. The black areas depict the countries of domicile of the 49,198 stocks which, divided into 24 groups, form the initial dataset of the pension-funds-held assets. The gray areas are not covered in the sample. Altogether, the sample covers almost he entire world except for Africa and the western part of Asia.
3.3.2 Liquidity Measures
In this paper I decided to measure liquidity in terms of the bid-ask spread. One way how to obtain the data is to rely on data providers, such as Bloomberg, which allow to directly obtain the quoted bid-ask spread. However, such data has certain
drawbacks. The quoted bid-ask spread must not necessarily be realistic as it does not take into account transaction delays (Foucault et al., 2013, p. 50-52). For in-stance, an effective spread might be more appropriate. Furthermore, Bloomberg quotes the end-of-day data which again might not be realistic since the condition when exchanges are closing can differ significantly from the rest of the day since intraday traders are forced to close their positions (McInish and Wood, 1992). A last drawback is that there is usually a subscription limit preventing from obtain-ing such an extensive data sample.
For the reasons above, I estimate the bid-ask spreads from the open-high-low-close (OHLC) prices which are easily and publicly available. More precisely, I use an estimation method introduced by Corwin and Schultz (2012) based on an assumption that the daily price range consists of the daily price volatility com-ponent and the bid-ask spread. Furthermore, they assume that within a short time-period, the volatility component is proportional to the length of the period, whereas the bid-ask spread is constant. It implies that a two-day period consists of the two-day volatility and two times the one-day spread. As a result, we are able to estimate the average daily bid-ask spread using price ranges of two consecutive trading days. A more detailed description of the estimation method is provided in Section A.2.
3.3.3 Sample Construction
Based on the Bloomberg screening, I download the historical prices of the indi-vidual stocks from Google Finance and Yahoo Finance data sources. The down-loaded data accounts for 42 thousand stocks and for about 111 million panel data observations. The raw dataset is cropped to match the period 2004–2016 when the data for margin calls are available. I then compute a monthly volatility of returns and a monthly price mean which are later used for further sorting. Fur-thermore, the data is cleaned to be suitable for the spread estimation. All the incomplete observations and the observations which do not form periods of at least two consecutive trading days are dropped. Finally, I estimate the bid-ask spreads.
In some cases, for instance if the daily price range is very narrow, the estima-tion might yield zero or negative spreads. If the range is very large, the spreads might be, on the other hand, overestimated. It is therefore appropriate to further clean the estimated spreads. The negative and zero values are disregarded
sim-ilarly as for example in Chordia et al. (2001). The right tail of the distribution is winsorized at the 95% level so the analysis is not biased by any extreme outliers.
Since one can expect the spreads to depend on certain factors such as price or volatility, I further divide the stocks into quintiles based on the monthly mean price and the monthly volatility of returns. Indeed, as depicted in Figure 3.3 the liquidity differs depending on the price and volatility bracket. More specifically, the mean bid-ask spread is higher approximately by 1 p.p. on average for the lowest price quintile and the highest volatility quintile than for the less volatile and more expensive stocks.
Figure 3.3: Liquidity Depending on Price and Volatility
P_Q2 P_Q3 P_Q4 P_Q5 V_Q1 V_Q2 V_Q3 V_Q4 V_Q5 mean mean P_Q2 P_Q3 P_Q4 P_Q5 V_Q1 V_Q2 V_Q3 V_Q4 V_Q5 mean mean P_Q2 P_Q3 P_Q4 P_Q5 V_Q1 V_Q2 V_Q3 V_Q4 V_Q5 mean mean mean 0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 6,0% 7,0%
Note: This figure shows the mean estimated daily bid-ask spreads of the 24 groups of assets further divided into subgroups based on price and volatility. The figure shows that the spreads vary depending on the price and volatility level. More precisely, the lowest price quantiles (P_Q1) and the highest volatility quantiles (V_Q5) generally ex-hibit approximately 1 p.p. higher spreads than the less volatile and more expensive assets. It implies that some of the assets might be more suitable for obtaining cash for the margin calls than others.
Finally, the estimated spreads are first differenced. The resulting liquidity sample consists of 24 georgraphic groups of stocks which contains 25 portfolios
that are monthly rebalanced according to the price and volatility quintiles. Alto-gether, the portfolios contain 40,866 individual stocks. The sample covers 2,914 trading days between the years 2004 and 2016 what yields 136,575 panel data ob-servations in total.
Since the current sample structure would require to estimate liquidity of 24 · 25 = 600 individual groups of assets, a further aggregation may be appropriate. Conveniently, albeit the fact that the level of the liquidity depends on the price and volatility quintiles, the first differences seem to be correlated across the quin-tiles.1I therefore aggregate the first differences within each country across the 25 portfolios which leaves me with 24 liquidity groups determined by the geographic location to be estimated.
In this thesis, for the lack of the necessary data, I assume equal weights of the individual stocks when aggregating them to the geographic groups. Using such an approach, I explicitly assume that the pension funds invest into small-cap and large-cap stocks equally. However, since the liquidity properties may depend on market capitalization of the given stock, the results might be biased. More specifically, the results might be overestimated as the liquidity of the small-cap stocks is generally worse and the pension funds are more likely to invest in a large cap stocks for their more suitable risk profile (Pastor and Stambaugh, 2001).
More appropriate approach would be to use historical market capitalizations of the individual stocks and construct a value-weighed portfolios rebalanced, for instance, on a monthly basis. However, the historical market capitalizations of worldwide stocks are not publicly available and I therefore have to use the equally-weighted approach.
The descriptive statistics of the first differences in absolute values are depicted in Table 3.2.
3.4 Liquidity Drivers
The variables that could possibly drive both liquidity and margin calls are selected based on the existing literature discussed in Chapter 2 and also based on the eco-nomic intuition related to the interest rate swap valuation. Generally, the vari-ables can be divided into the following groups.
Table 3.2: Descriptive Statistics of Liquidity Data
Group Mean Median SD P25 P75 N
Austraila 23.07 13.07 37.86 5.87 23.55 2844 Canada 22.68 14.24 33.49 6.58 25.98 2850 China 20.37 12.1 25.98 5.35 25.02 2852 Eurozone 7.97 5.34 10.58 2.45 9.95 2852 Hong Kong 25.16 16.16 31.15 7.43 29.47 2852 India 17.41 12.26 19.86 5.67 22.81 2852 Indonesia 46.14 18.46 84.79 7.61 44.7 2789 Japan 14.77 5.35 26.88 2.40 11.46 2850 Latin America 14.73 10.24 20.23 4.79 18.47 2851 Malaysia 19.63 14.88 20.7 6.86 26.37 2851 Mexico 26.57 17.83 34.91 8.11 33.99 2823 Netherlands 19.18 13.31 27.12 6.23 24.23 2833 Pac. Dev. 13.57 7.05 22.87 3.32 14.30 2846 Pac. Em. 24.29 15.6 32.91 7.281 30.22 2849 Russia 37.41 25.42 40.69 11.22 49.26 2829 Singapore 20.64 15.52 25.17 7.23 27.16 2850 Sweden 21.55 14.51 34.95 6.46 26.08 2842 Switzerland 16.6 10.09 31.24 4.539 18.49 2837 Thailand 18.41 13.61 21.41 6.24 24.3 2850 Turkey 16.01 10.45 19.16 4.78 19.79 2814 Taiwan 12.87 6.14 20.99 2.82 12.73 2847 UK 17.39 10.83 28.11 4.83 20.71 2838 USA 29.13 14.01 52.99 6.12 27.04 2851 Vietnam 15.58 10.9 21.69 5.07 19.56 2851
Note: This table contains descriptive statistics of the absolute values of the daily first differences in the liquidity of the individual groups of assets that form my sample. The data is reported in absolute values because otherwise, due to the stationarity of the series, the means would be zero and would not therefore provide much information. The data is reported in basis points. The average daily change in the spreads ranges from 8 basis points for EU assets to 46 basis points for Indonesian assets. The median values are reasonably close to the mean values. The standard deviations are propor-tional to the mean values. That is, the EU assets exhibit SD of 10.6 basis points, while the Indonesian assets exhibits SD of 85 basis points. Given the different mean values, one may expect that the liquidity response to the margin call could differ across the groups as well.
3.4.1 Interest Rate Based Variables
This group contains variables derived from short-term and long-term interest rate. In particular, they are the daily first differences in a central bank overnight rate and the daily first difference in a term spread (difference between the over-night rate and a 10-year government bond yield).2 In case the central bank rate is not available, I use the daily first differences in an interbank overnight rate in-stead. Additionally, I use volatility of a 10-year government bond as a proxy for the interest rate risk. The volatility is computed as a 5-day moving average of a 5-day standard deviation of the yields. The moving averages are used to smooth out any short-lasting shocks similarly as in Chordia et al. (2001). The period of 5 days reflects the length of a standard business week.
3.4.2 Equity Based variables
This group contains variables derived from equity indices and represents the per-formance and risk of the whole equity market. The variables are a 5-day moving average of the daily returns on the equity index, a 5-day standard deviation of the daily returns and a dummy variable which takes value of 1 when the moving average of the returns is negative and 0 otherwise. Such a dummy variable then denotes the presence of a bear market. The reason for the moving averages is the same as in the previous subsection.
3.4.3 Macroeconomic Indicators
This group contains variables constructed based on periodic announcements of values of GDP, CPI and unemployment. In particular, they are the daily first dif-ferences in the announced value and the daily first difdif-ferences in the expectation surprise (difference between the announced value and the survey consensus).3 Since the data are not announced daily, the variables take an actual value only on the announcement dates and 0 othervise. Furthermore, I also create a dummy variables denoting the dates of the given announcement similar as used in Chor-dia et al. (2001).
2Together, the overnight rate and the term spread, they also represent the long-term interest
rate.
3Together, the announced value and the surprise, they also represent the survey consensus
3.4.4 Seasonality Variables
Among these belong variables such as the dummy variables denoting weekdays (Monday to Thursday) which allows us to inspect the seasonal patterns in the data.
∗ ∗ ∗
The first three groups of variables are obtained individually for each of the geo-graphic groups introduced in Subsection 3.3.1, while the seasonality variables are common for all the groups. The initial set of all the possible variables is summa-rized in Table 3.3. The data are taken either from Bloomberg Terminal or from databases provided by central banks of the given countries. A detailed overview of the sources is presented in Table A.4 and in Table A.5. Table 3.4 contains de-scriptive statistics for a selected set of countries that are used in the main model later.
Table 3.3: Overview of Liquidity Drivers
Country Specific General
Interest Rate Based Equity Based Macroeconomic Seasonality
Overnight Rate Index Return CPI_act Monday
Term Spread Index Volatility CPI_surp Tuesday
IR Volatility Bear Market GPD_act Wednesday
GDP_surp Thursday
UN_act Global Crisis UN_surp
CPI GDP
UN
Note: This table provides an overview of the variables that were selected as the possi-ble drivers of both liquidity and margin calls. The variapossi-bles fall into three categories. The interest rate based variables represent the short-term interest rate, the long-term interest rate, and the interest rate volatility. They reflect the interest rate environment in general. The equity based variables reflect returns, volatility, and direction of the equity markets. The macroeconomic variables reflect changes in the macro indica-tors and also the expectations of the invesindica-tors. Finally, the last group of variables are the seasonality dummy variables.
The mean overnight rate ranges from 4.3% in Australia to 0.15% in Japan known for its low interest rates. The median of the overnight rate is always below its mean suggesting that the low interest rates prevail. Along with the minimum values close to or even below zero, the data reflect the recent global environment of very low interest rates. According to the term spreads, the mean yield of the 10-year government bonds is generally up to 2% higher than the mean of the overnight rate. However, some of the countries have minimum value of the term spread below zero suggesting an inverted yield curve at some point in time.
The positive mean values of the CPI and GDP changes in all the cases suggest that on average, there is an economic growth accompanied by slightly increas-ing inflation throughout the whole observed period. The best performer in terms of employment is Switzerland with 3.5% of average unemployment. The worst labour situation is in EU where, on average, almost 10% is unemployed. Inter-esting fact is, that the mean values of the announcement surprises are generally close to zero suggesting that the analysts are, on average, able of decent forecast-ing.
The mean value of the dummy variable denoting the presence of bear mar-ket is always slightly above 0.40 meaning that on average, the stock marmar-kets are growing.
Table 3.4: Descriptive Statistics of Selected Liquidity Drivers
Mean Median SD Min Max N Australia
Overnight Rate 4.304 4.250 1.576 2.000 7.250 2876 Term Spread 0.357 0.175 0.889 -1.940 2.860 2876 IR Volatility 0.009 0.000 0.046 0.000 0.617 2876 CPI Actual (YoY) 2.669 2.600 0.876 1.200 5.000 2876 CPI Surprise -0.023 0.000 0.250 -0.600 0.600 2876 GDP Actual (QoQ) 0.583 0.600 0.480 -1.200 1.600 2876 GDP Surprise 0.014 0.000 0.284 -0.700 0.700 2876 Unemp. Actual 5.222 5.200 0.596 4.000 6.400 2876 Unemp. Surprise -0.048 0.000 0.146 -0.500 0.400 2876 Index Return 0.001 0.000 0.004 -0.032 0.024 2876 Index Volatility 0.009 0.008 0.005 0.001 0.056 2876 Bear Market 0.444 0 0.496 0 1 2876 European Union Overnight Rate 2.319 1.750 1.526 0.300 5.250 2876 Term Spread 0.561 0.501 0.794 -1.171 2.504 2876 IR Volatility 0.007 0.000 0.037 0.000 0.647 2876 CPI Actual (MoM) 0.176 0.200 0.428 -1.600 1.400 2876 CPI Surprise 0.000 0.000 0.054 -0.100 0.200 2876 GDP Actual (QoQ) 0.166 0.300 0.605 -2.500 1.000 2876 GDP Surprise 0.001 0.000 0.061 -.0100 0.200 2876 Unemp. Actual 9.668 9.900 1.668 6.900 12.200 2876 Unemp. Surprise -0.008 0.000 0.103 -0.300 0.400 2876 Index Return 0.000 0.001 0.005 -0.047 0.032 2876 Index Volatility 0.010 0.008 0.007 0.001 0.712 2876 Bear Market 0.441 0 0.497 0 1 2876 United Kingdom Overnight Rate 2.116 0.555 2.164 0.383 6.794 2876 Term Spread 1.313 1.507 1.448 -2.315 3.870 2876 IR Volatility 0.048 0.002 0.113 0.000 1.293 2876 CPI Actual (MoM) 2.470 2.500 1.191 -0.100 5.200 2876 CPI Surprise 0.021 0.000 0.174 -0.400 0.600 2876 GDP Actual (YoY) 1.157 1.800 2.225 -5.500 3.300 2876 GDP Surprise -0.049 0.000 0.205 -0.600 0.400 2876 Unemp. Actual 6.537 6.300 1.246 4.700 8.400 2876 Unemp. Surprise -0.006 0.000 0.094 -0.200 0.200 2876 Index Return 0.000 0.001 0.005 -0.043 0.034 2876 Index Volatility 0.010 0.008 0.007 0.001 0.064 2876 Bear Market 0.440 0 0.496 0 1 2876
USA
Overnight Rate 1.436 0.160 1.953 0.040 5.410 2876 Term Spread 1.771 1.970 1.210 -0.850 3.810 2876 IR Volatility 0.047 0.015 0.099 0.000 1.463 2876 CPI Actual (MoM) 0.152 0.200 0.372 -1.700 1.200 2876 CPI Surprise -0.008 0.000 0.130 -0.400 0.400 2876 GDP Actual (QoQ) 2.039 2.500 2.44 -6.300 5.600 2876 GDP Surprise -0.049 0.000 0.309 -1.100 0.700 2876 Unemp. Actual 6.805 6.300 1.869 4.400 10.200 2876 Unemp. Surprise -0.033 0.000 0.149 -0.500 0.400 2876 Index Return 0.000 0.001 0.005 -0.039 0.036 2876 Index Volatility 0.010 0.008 0.008 0.002 0.076 2876 Bear Market 0.428 0 0.495 0 1 2876 Japan Overnight Rate 0.147 0.081 0.161 0.000 0.715 2876 Term Spread 0.974 1.033 0.405 0.003 1.990 2876 IR Volatility 0.010 0.005 0.020 0.000 0.245 2876 CPI Actual (YoY) 0.319 0.200 1.192 -2.500 3.700 2876 CPI Surprise 0.017 0.000 0.094 -0.300 0.300 2876 GDP Actual (YoY) -0.785 -0.800 1.847 -9.000 3.400 2876 GDP Surprise -0.216 0.000 1.227 -8.200 1.010 2876 Unemp. Actual 4.226 4.100 0.548 3.100 5.700 2876 Unemp. Surprise -0.023 0.000 0.156 -0.500 0.300 2876 Index Return 0.000 0.001 0.006 -0.043 0.033 2876 Index Volatility 0.012 0.010 0.008 0.001 0.086 2876 Bear Market 0.446 0 0.497 0 1 2876 Switzerland Overnight Rate 0.418 0.025 0.830 -1.693 2.621 2876 Term Spread 1.202 1.114 0.547 -0.110 2.587 2876 IR Volatility 0.055 0.019 0.096 0.001 1.402 2876 CPI Actual (YoY) 0.347 0.200 1.051 -1.400 3.100 2876 CPI Surprise -0.037 0.000 0.182 -0.500 0.500 2876 GDP Actual (YoY) 0.379 0.400 0.386 -0.800 1.000 2876 GDP Surprise 0.098 0.100 0.301 -0.500 0.700 2876 Unemp. Actual 3.256 3.200 0.466 2.300 4.500 2876 Unemp. Surprise -0.006 0.000 0.061 -0.200 0.100 2876 Index Return 0.000 0.001 0.005 -0.049 0.030 2876 Index Volatility 0.009 0.008 0.006 0.002 0.078 2876 Bear Market 0.437 0 0.496 0 1 2876
Note: The table above contains descriptive statistics of the independent variables for the asset groups Australia, EU, UK, USA, Japan and Switzerland, which are later used in the main model. The mean overnight rate ranges from 4.3% (Aus.) to 0.15% (Jap.). The medians below means and low or even negative minimum values suggest that low interest rates prevail. The term spreads are generally up to 2%. However, the neg-ative minimum values suggest the presence of an inverted yield curve at some points in time. The positive values of the GDP and CPI changes suggest that on average, there is an economic growth accompanied by slightly increasing inflation. The mean level of unemployment ranges from 3.5% (CH) to 10% (EU). The mean values of the announcement surprises are generally close to zero suggesting that the analysts are, on average, able of a decent forecasting. The mean value of the variable Bear Market below 0.5 implies that more than 50% of time, the equity markets are in an uptrend.
Methodology
4.1 Correlation
The first step of the analysis is to inspect whether the margin calls tend to coincide with times when the pension-fund-held assets are particularly illiquid. For this task, I employ the Pearson (1896) correlation coefficient defined as
ρi j=
σi j
σiσj
,
whereσi j is the covariance between the i th and j th variable andσi is the
stan-dard deviation of the given variable. More precisely, I take the proxy variable for the margin calls introduced in Section 3.2 and I compute its correlation with the estimated liquidity and its lags and leads across the individual groups of assets. This way, I obtain the following matrix with the correlation coefficients:
ρ−5,1 ρ−5,2 · · · ρ−5, j ρ−4,1 ρ−4,2 · · · ρ−4, j .. . ... . .. ... ρ5,1 ρ5,2 · · · ρ5, j , (4.1)
where the columns represent the individual groups of assets and the rows are the particular lags or leads. For instance,ρ5,1is the correlation of the margin calls and
the liquidity of the first asset group lagged by 5 days.
There are two particular reasons for inspecting not only the current correla-tion but also the lags and the leads. First, knowing the liquidity situacorrela-tion around the margin call event might be helpful when choosing the right strategy for ob-taining cash to fill the margin call. Second, my sample covers equities listed on
exchanges in different parts of the world. Since the trading hours differs for dif-ferent markets, the lags and leads can be used to account for these differences (Copeland and Copeland, 1998).
Further, I test the significance of each of the coefficients using the two-tailed test
H0: ρi , j= 0 against H1: ρi , j 6= 0 i ∈ {−5, . . . , 5} ; j ∈ {1, . . . , n} ,
where the test statistic
t = rr n − 2
1 − r2
follows a Student’s t -distribution with n − 2 degrees of freedom.
I then use the obtained p-values to mask the matrix from (4.1) so it, for report-ing purposes, contains only the significant correlations. The final structure of the correlation matrix is the following:
C = (ci j) = ci j= ρi j if p-vali j< 0.05, ci j= 0 otherwise.
This matrix provides us with information on whether the margin calls coincide with the illiquidity or not. More specifically, a positive value ci j suggests that the
illiquidity of the i th asset group lagged by j days exhibits a significant correlation with the margin calls variable. On the other hand, a negative coefficient would suggest, that the particular group of assets is actually more liquid when the mar-gin call occurs.
It is however important to stress that the potential relationship suggested by statistically significant correlation does not necessarily imply a causal relation-ship. In any case, the economic significance should be subject to further research using more sophisticated methods which are employed in the subsequent sec-tions.
4.2 Probit Model
The next step of my research is to elaborate the results of the correlation analysis more in detail and to find out whether it points to a certain underlying economic relationship. One explanation of a potential significant correlation between liq-uidity and margin calls could be that there are certain economic factors that drive both liquidity and margin calls.
To find out whether such a relationship is plausible, I regress the proxy vari-able for the margin calls on the liquidity drivers introduced in Section 3.4. Once the model is estimated, I assess the importance of the individual drivers by test-ing their statistical significance. Since the dependent variable is a binary variable, I employ a probit model estimated using maximum likelihood estimation. In par-ticular, the model has the following form:
Prob(Y = 1|X ) = Φ(X β),
where Y is a vector (y1, . . . , yt), X is a matrix of the exogenous liquidity drivers and
Φ(·) is a cumulative distribution function (CDF) of the standard normal distribu-tion. The advantage of such a model structure is thatΦ(·) is a function projecting R on (0,1). Consequently, after plugging the outcome of the inner linear model
Y∗= X β into Φ, the model always yields value between 0 and 1. The obtained value can be then conveniently interpreted as a probability of Y being 1 given the set of variables X . In particular, I can compute the probability of a margin call given the particular values of the liquidity drivers.
Initially, the matrix X contains all the liquidity drivers from Chordia et al. (2001) or Chordia et al. (2005) and additionally a few variables that are, based on the reasoning given in Chapter 1, expected to affect the probability of margin calls as well. Including all the variables, however, may potentially lead to an overfitted model. In order to avoid overfitting, in practice, we usually compromise between the model’s explanatory power and a reasonable number of the independent vari-ables. To select the optimal model, one can employ for instance the Akaike (1973) (AIC) and the Schwarz-Bayesian (BIC) (Schwarz et al., 1978) information criteri-ons. These criterions are defined as
AIC=2m − 2L , BIC=m · log(n) − 2L ,
where m is the number of the independent variables, n is the number of obser-vations andL is the maximized log-likelihood from the model estimation. The AIC and BIC criterions allow to compare multiple model specifications based on their explanatory power and based on the number of the independent variables they contain. In particular, both the measures prioritize the models with high ex-planatory power (highL ) but at the same time, they penalize for every additional independent variable. In general, the lower the value of the criterion is, the better the given model is compared to its alternatives.
Once I select and estimate the final model, I test the significance of the indi-vidual drivers using the following t -tests
H0: βi= 0 i ∈ {1, . . . , n} .
Should any of the coefficients be significant and positive, one can conclude that an increase in the value of the given liquidity driver increases the probability of margin call as well. I also test the joint significance of all the coefficients using the
F -test:
H0: β1= β2= · · · = βn= 0,
to assess the overall explanatory power of the model. In case we fail to reject the null hypothesis, one can conclude that the given drivers do not drive the margin calls.
Furthermore, once the model is estimated, I compute the marginal effects of the individual variables as
∂Prob(Y = 1|X ) ∂xi
= Φ0(Xβ)βi= φ(X β)βi,
where φ(·), the derivative of Φ(·), is a probability density function (PDF) of the standard normal distribution. The marginal effect can be interpreted as a change in the conditional probability of the dependent variable being 1 induced by a unit change of the respective explanatory variable.
Finally, I use the marginal effects to analyse which of the drivers affect the probability of margin calls while holding the values of the rest of the variables fixed. Although there is no ultimate rule for what values to fix the variables at, a common practice is to use their mean values. I therefore use the mean values. However, in Section 6.1, I discuss the robustness of my results and I try using some alternative default values as well.
4.3 VAR Model
The last step of the thesis is to put the results from Section 4.1 and Section 4.2 together and analyse what is happening to the liquidity when a margin call oc-curs. Combining and extending the approach used in Chordia et al. (2001) and in Chordia et al. (2005), I employ a VAR model with exogenous variables. The model is specified as follows:
LQ1t = n P i =1 k P j =1β1i j LQi ,t −j+ l P p=1δ1p xp t+ u1t, .. . LQnt= n P i =1 k P j =1βni j LQi ,t −j+ l P p=1δnp xpt+ unt, (4.2)
whereδi p= 0 if xp tdoes not represent a local variable. LQ1, . . . , LQnare the daily
first differences of the liquidity of the particular asset groups 1 . . . 24. X1, . . . , Xl
are the exogenous variables representing the liquidity drivers. Some of the ex-ogenous variables in (4.2) are explicitly constrained to zero. The reason for such a model structure is that one expects the local liquidity to be driven predomi-nantly by the local variables and not by the foreign ones. For instance, there is not much economic sense in the Indonesian interest rate driving liquidity of the US assets. Such constraints may also decrease the chance of obtaining misleading results due to a possible multicollinearity of the respective variables across the individual countries. However, the structure of the VAR model still allows the en-dogenous variables to affect each other and one can therefore study commonality in liquidity and spillovers between the different markets.
Selection of the optimal model is done using a general-to-specific approach combined with the information criterions. That is, I start with a full set of the exogenous variables and a sufficient amount of lags of the endogenous variables. I then drop the not-significant variables and lags based on their t -statistics one by one while comparing the information criterions as in Section 4.2.
Once the final model is estimated I use the results to inspect the properties of the liquidity of the given assets. First, a significant coefficient of the i th exogenous variable in the j th equation, i.e. rejecting the hypothesis:
H0: δi j= 0,
suggests that the i th variable affects the liquidity of the j th group of assets. Fur-ther, a significant coefficient of the j th lagged endogenous variable in the j th equation, i.e. rejecting the hypothesis:
H0: βj j= 0,
suggests an autocorrelation in the liquidity of the j th group of assets. Finally, a significant coefficient of the i th (lagged) endogenous variable in the j th equation, i.e. rejecting the following hypothesis:
H0: βi j= 0,
suggests a relationship between the liquidity of the i th and the j th group of as-sets. More specifically, a positive coefficient implies commonality in liquidity. A negative coefficient, on the other hand, implies spillovers.
Utilizing all the above-mentioned together, I analyze the impulse-response function described for instance by Koop et al. (1996). The impulse-response func-tion can be used to analyze the response of the individual variables to a one-time shock. This way, I can simulate a shock to one of the exogenous variables, previ-ously identified as important for the margin calls, and investigate what happens to the liquidity of the individual asset groups.
Results
5.1 Correlation of Margin Calls and Liquidity
The first hypothesis of interest is whether the margin calls tend to coincide with times when the pension-fund-held assets might be illiquid. To answer that ques-tion I employ a method based on the Pearson correlaques-tion coefficient introduced in Section 4.1. More specifically, I focus on whether the depletion of the margin account is correlated with an increased illiquidity.
I first inspect the correlations of the assets divided into the geographic groups described in Chapter 3 and I find out that the majority of the groups exhibits a significant correlation. I then aggregate the liquidity measure of these countries using equal weights and inspect the correlations again. I arrive at a correlation pattern as depicted in Figure 5.1.
In general, there is a significant positive correlation between the depletion of the margin account and the illiquidity of the assets lagged by three days. The fig-ure suggests one exception consistent across all of the price quintiles. The assets in the lowest volatility quintile exhibit little to none correlation with the depletion of the margin account. The rest of the assets shows significant positive correlation up to 40%. Based on the classification from Evans (1996), we can say that there is a moderate positive relationship between the illiquidity and the depletion of the margin account. More precisely, Figure 5.1 suggests that some of the assets might become illiquid three days after there is a loss of margin.
One possible reason for such a difference in timing might be that margin calls and margin in general are intended to cover for the changing value of the traded position without delay whereas, as described in Chapter 2, liquidity reflects the beaviour of dealers and market makers. Consequently the margin call might
fol-Figure 5.1: Correlation of Margin Calls and Liquidity
Note: This figure depicts correlation of the variable denoting the depletion of the mar-gin account with the daily firs differences of the estimated bid-ask spreads aggregated across all the 24 groups of assets. For the sake of clarity, the figure shows only the sta-tistically significant correlations, the not-significant ones are reported as 0. There is a moderate significant correlation up to 0.40 on the third lag meaning that some of the assets may become illiquid approximately 3 days after there is a significant outflow of margin. However, the lowest price qintiles across all the volatility quintiles do not exhibit any correlation with the margin depletion.
low the change in market condition immediately while it might take some time for the dealers to adapt to the changing market, hence the lag.
Finding a significant relationship between liquidity and margin calls speaks in favor of further research. However, there is already one interesting implication at this stage. In case the change in liquidity was indeed lagged in terms of days after the margin call, the optimal strategy for pension funds might be to start selling their assets only after the margin call occurs but before the liquidity decreases. Furthermore, for instance CME Group1, a global provider of clearing services for OTC-traded derivatives, requires the margin to be transferred the same day the margin call is triggered. Given such a tight schedule, the liquidity conditions 3 days after the margin call might be irrelevant in the first place.
A more detailed overview of the results can be found in Table 5.1 where I report all the correlation coefficients with their respective p-values.
1See http://www.cmegroup.com/education/files/Clearing_Transacton_Timeline.
